Preheat the oven to 400°F (204°C) and line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, salt, cinnamon, and nutmeg until well combined.
Grate the frozen butter into the flour mixture. Use a pastry cutter or two knives to work it in until the mixture resembles coarse crumbs with pea-sized pieces of butter throughout.
Dice the peaches and toss them with 1 tablespoon of the flour mixture. Add them to the bowl and gently fold to combine.
In a small bowl, whisk together the egg, sourdough discard, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and gently stir until the dough just begins to come together. Add only enough buttermilk or kefir, if needed, to bring the dough together.
Turn the dough out onto a lightly floured surface and gently pat it into a circle about 1 to 1½ inches thick. Cut into 8 wedges and transfer them to the prepared baking sheet. Chill for 20–30 minutes.
Brush the tops of the chilled scones with cream, then sprinkle generously with brown sugar.
Bake for 15–18 minutes, or until the scones are risen and golden brown. Transfer to a wire rack and let cool completely.
Whisk together the glaze ingredients and drizzle over the cooled scones before serving.